If \(K\)  is dropped from the notation, it always means \(K=X\) . We note that for any \(\varphi , \phi \in C(X,\mathbb {R})\)  (see [1]})
\(\begin{aligned}|P(d, T, \varphi , \epsilon , K)-P(d, T, \phi , \epsilon , K)|\le \Vert \varphi -\phi \Vert \end{aligned}\) 
